The relationships of solar flares with both sunspot and geomagnetic activity

The relationships between solar flare parameters （total importance, time duration, flare index, and flux） and sunspot activity （R z ） as well as those between geomagnetic activity （aa index） and the flare parameters can be well described by an integral response model with the response time scales of about 8 and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with R z , of aa with the flare parameters, and of aa with R z based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to R z , aa to the flare parameters, and aa to R z at their peaks in a solar cycle can be predicted in part by this model （82%, 47%, and 78%, respectively）. These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energy in the past through a time decay factor. The above results may help us to understand the mechanism of solar flares and to improve the prediction of the solar flares.

Sunspot Group Detection and Classification by Dual Stream Convolutional Neural Network Method

The automatic detection and analysis of sunspots play a crucial role in understanding solar dynamics and predicting space weather events.This paper proposes a novel method for sunspot group detection and classification called the dual stream Convolutional Neural Network with Attention Mechanism(DSCNN-AM).The network consists of two parallel streams each processing different input data allowing for joint processing of spatial and temporal information while classifying sunspots.It takes in the white light images as well as the corresponding magnetic images that reveal both the optical and magnetic features of sunspots.The extracted features are then fused and processed by fully connected layers to perform detection and classification.The attention mechanism is further integrated to address the“edge dimming”problem which improves the model’s ability to handle sunspots near the edge of the solar disk.The network is trained and tested on the SOLAR-STORM1 data set.The results demonstrate that the DSCNN-AM achieves superior performance compared to existing methods,with a total accuracy exceeding 90%.

Low-dimensional chaos and fractal properties of long-term sunspot activity

Two primary solar-activity indicators- sunspot numbers （SNs） and sunspot areas （SAs） in the time interval from November 1874 to December 2012 - are used to determine the chaotic and fractal properties of solar activity. The results show that （1） the long-term solar activity is governed by a low-dimensional chaotic strange attractor, and its fractal motion shows a long-term persistence on large scales; （2） both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of SNs, implying that the dynamical system of SAs is more chaotic and complex than SNs; （3） the predictions of solar activity should only be done for short- to mid-term behaviors due to its intrinsic complexity; moreover, the predictability time of SAs is obviously smaller than that of SNs and previous results.

Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number,Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, Di, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show （1） for 46 months （94%） of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri - Di plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level a = 5%, and for 36 months （73%） the fitting is even better, for a = 1%; （2） time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; （3） the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log/~ = 0.704 lnDi - 0.291.

Periodic variation and phase analysis of grouped solar flare with sunspot activity

Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycles.Here we report the statistical analysis of grouped solar flare(GSF) and sunspot number(SN) during the time interval from January 1965 to March 2009.We find that,(1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity,the quasi-biennial oscillation(QBO),and the eleven-year Schwabe cycle(ESC),but the specific values are not absolutely identical;(2) the ESC signal of GSF lags behind that of SN with an average of 7.8 months during the considered time interval,which implies that the systematic phase delays between GSF and SN originate from the inter-solar-cycle signal.Our results may provide evidence about the storage of magnetic energy in the corona.

ENSO Index Variations and Links with Solar and Volcanic Activity

In this paper, we investigated the Oceanic Niño Index (ONI), for simplicity called in this paper an El Nino Southern Oscillation (ENSO) index in 1950-2023 by applying the wavelet spectral transform and the IBM SPSS correlations analysis. ONI follows the three months’ current measurements of the average temperature of the sea surface in the East-Central tropical part of the Pacific Ocean nearby the international line of the date change over the average sea surface temperature over the past 30 years. The ENSO index is found to have a strong (>87%) correlation with the Global Land-Ocean Temperature (GLOT). The scatter plots of the ENSO-GLOT correlation with the linear and cubic fits have shown that the ENSO index is better fit by the cubic polynomial increasing proportionally to a cubic power of the GLOT variations. The wavelet analysis allowed us to detect the two key periods in the ENSO (ONI) index: 4 - 5 years and 12 years. The smaller period of 4.5 years can be linked to the motion of tectonic plates while the larger period of 12 years is shown to have a noticeable correlation of 25% with frequencies of the underwater (submarine) volcanic eruptions in the areas with ENSO occurrences. Not withholding any local terrestrial factors considered to contribute to the ENSO occurrences, we investigated the possibility of the volcanic eruptions causing ENSO to be also induced by the tidal forces of Jupiter and Sun showing the correlation of the underwater volcanic eruption frequency with the Jupiter-Earth distances to be 12% and with the Sun-Earth distances, induced by the solar inertial motion, in January, when the Earth is turned to the Sun with the southern hemisphere where the ENSO occurs, to become 15%. Hence, the underwater volcanic eruptions induced by tidal forces of Jupiter and Sun can be the essential additional factors imposing this 12 year period of the ENSO (ONI) index variations.

The Decay Process of an α-configuration Sunspot

The decay of sunspot plays a key role in magnetic flux transportation in solar active regions(ARs).To better understand the physical mechanism of the entire decay process of a sunspot,an α-configuration sunspot in AR NOAA 12411 was studied.Based on the continuum intensity images and vector magnetic field data with stray light correction from Solar Dynamics Observatory/Helioseismic and Magnetic Imager,the area,vector magnetic field and magnetic flux in the umbra and penumbra are calculated with time,respectively.Our main results are as follows:(1) The decay curves of the sunspot area in its umbra,penumbra,and whole sunspot take the appearance of Gaussian profiles.The area decay rates of the umbra,penumbra and whole sunspot are-1.56 MSH day^(-1),-12.61 MSH day^(-1) and-14.04 MSH day^(-1),respectively;(2) With the decay of the sunspot,the total magnetic field strength and the vertical component of the penumbra increase,and the magnetic field of the penumbra becomes more vertical.Meanwhile,the total magnetic field strength and vertical magnetic field strength for the umbra decrease,and the inclination angle changes slightly with an average value of about 20°;(3) The magnetic flux decay curves of the sunspot in its umbra,penumbra,and whole sunspot exhibit quadratic patterns,their magnetic flux decay rates of the umbra,penumbra and whole sunspot are-9.84 × 10^(19)Mx day^(-1),-1.59 × 10^(20)Mx day^(-1) and -2.60 × 10^(20)Mx day^(-1),respectively.The observation suggests that the penumbra may be transformed into the umbra,resulting in the increase of the average vertical magnetic field strength and the reduction of the inclination angle in the penumbra during the decay of the sunspot.

The Formation and Evolution of the Sun and the Source of Star Energy as Well as the Sunspots and Flares of the Sun

Nebula theory is the most widely accepted hypothesis about the formation and evolution of the Solar System. This theoryholds that the Sun is formed from a collapsed gas cloud 4.57 billion years ago;when the core temperature of the gas cloud rises to 10million K, the thermonuclear reaction of hydrogen fusion into helium is ignited, then the Sun become a star;once the hydrogen in thecore is exhausted, the life of the star will end. But the limited hydrogen element obviously cannot satisfy such a long-termthermonuclear reaction, in order to sustain long-term thermonuclear reactions, a steady stream of fuel must be obtained from space.So the existing hypothesis about the formation and evolution of the Solar System has serious defects. Thus the author has studied theformation of the Moon, the Earth and the Sun, and discovered the formation of the Sun and the real source of star energy. The authorcould also explain many solar activity phenomena such as sunspots, flares, prominences, etc.

Magnetic cycles of Sun-like stars with different levels of coronal and chromospheric activity——comparison with the Sun

The atmospheric activity of the Sun and Sun-like stars is analyzed involving observations from the HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories and the Magellan Planet Search Program at the Las Campanas Observatory. We show that for stars of E G and K spectral classes, the cyclic activity, similar to the 11-yr solar cycle, is different： it becomes more prominent in K-stars. Comparative study of Sun-like stars with different levels of chromospheric and coronal activity confirms that the Sun belongs to stars with a low level of chromospheric activity and stands apart among these stars by its minimum level of coronal radiation and minimum level of variations in photospheric flux.

Multiple cycles of magnetic activity in the Sun and Sun-like stars and their evolution

The wavelet transform method for high-quality time-frequency analysis is applied to sets of observations of relative sunspot numbers and stellar chromosphere fluxes of 10 Sun-like stars. Wavelet analysis of solar data shows that in a certain interval of time there are several cycles of activity with pe- riods of duration which vary considerably from each other： from quasi-biennial cycles to lO0-yr cycles. Cyclic activity was detected in almost all Sun-like stars that we examined, even those that previously were not considered as stars with cyclic activity according to analysis using a Scargle periodogram. The durations of solar and stellar cycles significantly change during the observation period.

Latitudinal migration of sunspots based on the ESAI database

The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices（ESAI）elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI＇s yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.

On the Imminent Regional Seismic Activity Forecasting Using INTERMAGNET and Sun-Moon Tide Code Data

In this paper we present an approach for forecasting the imminent regional seismic activity by using geomagnetic data and Earth tide data. The time periods of seismic activity are the time periods around the Sun-Moon extreme of the diurnal average value of the tide vector module. For analyzing the geomagnetic data behaviour we use diurnal standard deviation of geomagnetic vector components F (North, East, Down) for calculating the time variance GeomagSignal. The Sun storm influence is avoided by using data for daily A-indexes (published by NOAA). The precursor signal for forecasting the incoming regional seismic activity is a simple function of the present and previous day GeomagSignal and A-indexes values. The reliability of the geomagnetic “when, regional” precursor is demonstrated by using statistical analysis of day difference between the times of “predicted” and occurred earthquakes. The base of the analysis is a natural hypothesis that the “predicted” earthquake is the one whose surface energy density in the monitoring point is bigger than the energy densities of all occurred earthquakes in the same period and region. The reliability of the approach was tested using the INTERMAGNET stations data located in Bulgaria, Panagurishte, PAG (Jan 1, 2008-Jan 29, 2014), Romania, Surlari, SUA (Jan 1, 2008-Jan 27, 2014), Italy, L’Aquila, AQU (Jan 1, 2008-May 30, 2013) in the time of EU IRSES BlackSeaHazNet (2011-2014) project. The steps of program for solving the “when, where and how” earthquake prediction problem are shortly described.

The causality between the rapid rotation of a sunspot and an X3.4 flare

Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in active region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neutral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field lines twisting in the photosphere. The twist is then transported into the corona and triggers flares.

Long-Term Sunspot Number Prediction based on EMD Analysis and AR Model

The Empirical Mode Decomposition （EMD） and Auto-Regressive model （AR） are applied to a long-term prediction of sunspot numbers. With the sample data of sunspot numbers from 1848 to 1992, the method is evaluated by examining the measured data of the solar cycle 23 with the prediction： different time scale components are obtained by the EMD method and multi-step predicted values are combined to reconstruct the sunspot number time series. The result is remarkably good in comparison to the predictions made by the solar dynamo and precursor approaches for cycle 23. Sunspot numbers of the coming solar cycle 24 are obtained with the data from 1848 to 2007, the maximum amplitude of the next solar cycle is predicted to be about 112 in 2011-2012.

Wavelet Analysis of Several Important Periodic Properties in the Relative Sunspot Numbers

We investigate the wavelet transform of yearly mean relative sunspot number series from 1700 to 2002. The curve of the global wavelet power spectrum peaks at 11-yr, 53-yr and 101-yr periods. The evolution of the amplitudes of the three periods is studied. The results show that around 1750 and 1800, the amplitude of the 53-yr period was much higher than that of the the 11-yr period, that the ca. 53-yr period was apparent only for the interval from 1725 to 1850, and was very low after 1850, that around 1750, 1800 and 1900, the amplitude of the 101-yr period was higher than that of the 11-yr period and that, from 1940 to 2000, the 11-yr period greatly dominates over the other two periods.

Low Dimensional Chaos from the Group Sunspot Numbers

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent （MLE） for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 （month^- 1）. Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.

Predicting the 25th solar cycle using deep learning methods based on sunspot area data

It is a significant task to predict the solar activity for space weather and solar physics. All kinds of approaches have been used to forecast solar activities, and they have been applied to many areas such as the solar dynamo of simulation and space mission planning. In this paper, we employ the long-shortterm memory(LSTM) and neural network autoregression(NNAR) deep learning methods to predict the upcoming 25 th solar cycle using the sunspot area(SSA) data during the period of May 1874 to December2020. Our results show that the 25 th solar cycle will be 55% stronger than Solar Cycle 24 with a maximum sunspot area of 3115±401 and the cycle reaching its peak in October 2022 by using the LSTM method. It also shows that deep learning algorithms perform better than the other commonly used methods and have high application value.

Periodicities in Solar Activity, Solar Radiation and Their Links with Terrestrial Environment

Solar magnetic activity is expressed via variations of sunspots and active regions varying on different timescales. The most accepted is an 11-year period supposedly induced by the electromagnetic solar dynamo mechanism. There are also some shorter or longer timescales detected: the biennial cycle (2 - 2.7 years), Gleisberg cycle (80 - 100 years), and Hallstatt’s cycle (2100 - 2300 years). Recently, using Principal Component Analysis (PCA) of the observed solar background magnetic field (SBMF), another period of 330 - 380 years, or Grand Solar Cycle (GSC), was derived from the summary curve of two eigenvectors of SBMF. In this paper, a spectral analysis of the averaged sunspot numbers, solar irradiance, and the summary curve of eigenvectors of SBMF was carried out using Morlet wavelet and Fourier transforms. We detect a 10.7-year cycle from the sunspots and modulus summary curve of eigenvectors as well a 22-year-cycle and the grand solar cycle of 342 - 350-years from the summary curve of eigenvectors. The Gleissberg centennial cycle is only detected on the full set of averaged sunspot numbers for 400 years or by adding a quadruple component to the summary curve of eigenvectors. Another period of 2200 - 2300 years is detected in the Holocene data of solar irradiance measured from the abundance of 14C isotope. This period was also confirmed with the period of about 2000 - 2100 years derived from a baseline of the solar background magnetic field, supposedly, caused by the solar inertial motion (SIM) induced by the gravitation of large planets. The implication of these findings for different deposition of solar radiation into the northern and southern hemispheres of the Earth caused by the combined effects of the solar activity and solar inertial motion on the terrestrial atmosphere is also discussed.

Prediction of Short Stellar Activity Cycles using Derived and Established Empirical Relations between Activity and Rotation Periods

In our previous work,we investigated the occurrence rate of super-flares on various types of stars and their statistical properties,with a particular focus on G-type dwarfs,using entire Kepler data.The said study also considered how the statistics change with stellar rotation period,which in turn,had to be determined.Using such new data,as a by-product,we found 138 Kepler IDs of F-and G-type main sequence stars with rotation periods less than a day(P_(rot)<1 day).On one hand,previous studies have revealed short activity cycles in F-type and G-type stars and the question investigated was whether or not short-term activity cycles are a common phenomenon in these stars.On the other hand,extensive studies exist which establish an empirical connection between a star's activity cycle and rotation periods.In this study,we compile all available Kepler data with P_(rot)<1 day,and rely on an established empirical relation between P_(cyc)and P_(rot)with the aim to provide predictions for very short 5.09≤P_(cyc)≤38.46 day cases in a tabular form.We propose an observation to measure P_(cyc)using a monitoring program of stellar activity(e.g.,activity-related chromospheric emission S-index)or a similar means for the Kepler IDs found in this study in order put the derived empirical relations between P_(cyc)and P_(rot)derived here to the test.We also propose an alternative method for measuring very short P_(cyc),using flare-detection algorithms applied to future space mission data.

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultane- ous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results： （a） fluctuations in the meridional circulation are more effective in producing grand minima; （b） both sudden and gradual initiations of grand minima are possible; （c） distributions of durations and waiting times between grand minima seem to be exponential; （d） the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an a-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this a-effect is suitably fine-tuned.